Question: Let $f(x) = -5x^{2}+5x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Explanation: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-5x^{2}+5x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -5, b = 5, c = 1$ $ x = \dfrac{-5 \pm \sqrt{5^{2} - 4 \cdot -5 \cdot 1}}{2 \cdot -5}$ $ x = \dfrac{-5 \pm \sqrt{45}}{-10}$ $ x = \dfrac{-5 \pm 3\sqrt{5}}{-10}$ $x =\dfrac{-5 \pm 3\sqrt{5}}{-10}$